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Does it matter how far you are in a virtual world network?
Majority of the studies have focused mainly on existing ties of a collaborative nature and within established organizational settings, but only a few studies studied the more free-form connections that appeared during the collaboration on virtual tasks and the immersive digital worlds enabled by technology. In present day’s digitally-networked environments, to what measure does distance still affect interaction? Focusing on existing ties in the physical world is important. But the role of proximity in establishing online collaborative relations in virtual worlds created by ICTs is also important. With the emergence of virtual worlds such as Second Life and online games, there is a significant change in the way we work and play. Most of the studies that have examined proximity and digital ties have mainly focused on informational ties such as connections formed on the micro-blogging site Twitter. But the effect of proximity in virtual interactions such as online collaborative ties which enable people to have more narrational relations in a virtual world remains relatively uncertain. With the scale and complexity of human collaboration in virtual worlds, there is an excellent opportunity to study the emergence and effectiveness of groups in complex social settings. Also, virtual worlds provide unparalleled data traces of individual interactions and behaviour that were not available in early days. Another fact to be considered is that online relations are dynamic and complex: some branch from previous personal ties and the rest are solely based on activities in virtual worlds. The role of proximity in online collaboration is an important factor to be considered. The influence of three dimensions of proximity on the formation of collaboration relations in a virtual world: space, time, and homophily are hypothesized. There have been lot of research on the effects of proximity on social and collaborative dynamics. There have been mixed findings that could be partially attributed to at least two factors: conceptual and methodological. Most of the existing studies conceptualize proximity in terms of geographic distance. But proximity can also be considered as a multidimensional concept. “virtuality” can be unpaked into four distinct components: geographic dispersion, electronic dependence, dynamic structure, and national diversity. geographic dispersion can also be viewed as a multidimensional conceptualization, including spatial, temporal, and configurational characteristics. Similarly, objective measures of distance include geographic distance, time distance (time zones), organizational distance, and cultural differences. Even with the implicit presence of some or all these dimensions, spatial proximity is the dominant factor in many studies. Proximity can be considered to be a multi-faceted concept that encompasses related but distinct dimensions. For example, two people who are located 1000 miles away may also be in different time zones and may have different individual characteristics. These factors contribute to their unique interaction patterns. In many cases, two or more than two dimensions of proximity exist together and exert influence on network dynamics together, but their mechanisms and effects cannot be separated unless each of those dimensions is carefully considered and examined in conjunction with others. Considering on a methodological standpoint, proximity is operationalized as a dichotomous variable: dyads or teams are either collocated or dispersed. This operationalization can cause a few problems because it does not realize that proximity should be measured in terms of degree in real life situations. For example, in case of a distributed team having members from two nearby cities is different from a transnational team whose members are located in two or more countries. Other advanced measures are required to show how proximity influences people's interaction patterns. Physical and psychological similarities between people play a major role in interpersonal attraction. For players' physical proximity in online games, distance constraints have been illuminated by the virtual world but time differences are still a cost of coordinating with other players. The three major aspects considered in the formation of online relations are spatial proximity (physical distance), temporal proximity (time zone difference), and homophily (social distance based on individual characteristics). Drawing upon the research on offline relations, a series of hypotheses are presented on the formation of online relations based on three exogenous factors: spatial proximity, temporal proximity, and homophily. '21.2 Long answer: ' ''21.2.1.Spatial proximity '' It is an old tradition to examine the impact of spatial proximity on communication.For long studies have been conducted on how spatial proximity affects constructs such as friendship, romantic relationships, and variables like the amount of communication. Their frequency of spontaneous communications between workers dropped drastically when the spatial distance between workers reached 30 m and beyond, 1. With the advent of communication technology, There is a need to investigate whether spatial proximity is still relevant with the surge in computer mediated communication. Studies have been performed on how individuals that know each other offline communicate online. There is not much knowledge on examining how individuals that do not know each other offline communicate when online. In general, individuals who are located closer to each other are more likely to communicate than individuals who are located farther away from each other. This is regardless of whether the communication is face-to-face or not. Even after taking into account organizational proximity and the factor of similarity in interests, individuals located closer together are more likely to collaborate with each other both face-to-face and by phone and email. One possible explanation for this can be that computer-mediated communications are more useful in augmenting, rather than replacing, face-to-face communication between people located closer to each other than those located farther apart. Spatial proximity has a significant and positive impact on the interactions of individuals in both face-to-face and computer-meditated contexts. Virtual worlds inherit the impact of spatial proximity that augments existing relations 3. This study will examine the impact of spatial proximity in virtual worlds where individual players distributed across geographical distances engage in various activities such as communication, economic transaction, and group collaboration. Hence, we propose the following hypothesis: Hypothesis 1. (Spatial proximity): Individuals who are proximate in geographical distance are more likely to interact with one another than those who are not proximate. To what extent is the impact of proximity linear? Most of the early studies considered short distances like the location of offices in the same building. It is pretty intuitive: if two people's offices are on the same floor, then they are the ones more likely to strike a hallway conversation than those who have it on different floors buildings. Reference 11 shows that residential proximity is a very good predictor of how often friends get together to socialize, however, the same mechanism may not become as intuitive as distance grows larger. To what extent can we argue that people are more likely to interact when they live within a shorter distance? In such a situation, we consider the cost of communication and commute. The travel time and expenses plays a role in reducing the likelihood of interaction when the transportation mode changes, e.g., from walking distance to driving distance. There is no linearity in the changes in travel and communication, but they tend to increase sharply when the distance becomes more than a short range. Hence, if the distances between individuals are large enough, there is a similar impact because the costs would remain largely at the same level. Hypothesis 2. Short distance: Individuals who are in close proximity are substantially more likely to interact with one another than those who are at medium or low proximity. ''21.2.2. Temporal proximity '' The previous hypotheses tell us about the spatial dimension of proximity characterized by geographical separation. Another perspective that needs to be considered is how space is less of an organizing principle than the costs associated with getting between places or communicating between places. For example, it is more “costly” for people without a car to travel to another city located 100 miles away than those who have access to a car. With extensive connectivity to networked computers and the pervasiveness of global teams, the communication cost perspective has led to shift the attention from spatial distance to temporal distance, referred to as temporal proximity in the current study, or namely, the overlap of waking hours. Temporal proximity is measured in terms of time zone difference. It is more costly for people who are in different time zones and hence share fewer waking hours to interact synchronously, compared with those who share more waking hours. Therefore, temporal proximity also affects the likelihood of communication, especially synchronous communication. Even though the influences of spatial proximity and temporal proximity are very distinct on the networks, most empirical studies do not consider the effects of these two forms of proximity simultaneously. While some teams are only spatially (but not temporally) dispersed, most global teams are confronted with both distances. Therefore, it is important to consider both spatial proximity and temporal proximity together when studying their impacts. Hypothesis 3. Temporal: Individuals who are proximate in time zone are more likely to interact with one another than those who have larger time zone differences. ''21.2.3. Homophily '' Individuals can have similar social characteristics such as gender and age otherwise known as homophily, meaning that the individuals are proximate in the social space. Homophily facilitates communication, which is exemplified by the old saying “birds of a feather flock together.” The word “homophily” was first coined by Lazarsfeld and Merton 6when referring to a tendency of people to be attracted to others who have similar attitudes, beliefs, and personal characteristics. Monge and Contractor 9 summarized two lines of theoretical underpinnings of homophily: the similarity-attraction hypothesis and the theory of self-categorization. The similarity-attraction hypothesis states that people are more likely to interact with those who have similar traits. The self-categorization theory states that people tend to self-categorize with regard to race, gender, socio-economic status, etc., and they differentiate between similar and dissimilar people based on such attributes. Homophily has received strong support from empirical research, in terms of gender 4, race 8, and status 7. Homophily, especially with regard to gender, ethnicity, and occupation, has been found as a critical factor of relationship formation in entrepreneurial teams , work team composition , and generally in the formation of social networks. The homophily theory suggests that people of the same attributes tend to interact with each other because of their common interests and similar background. Players' demographic attributes such as gender and age may not always be visible, but other players may still be able to perceive behavioural patterns related to these attributes. For example, male players are more likely to choose male characters and engage in combat activities etc. Also, online interactions and social activities may help players exchange some personal information and become familiar with each other. Therefore, in virtual worlds, demographic attributes such as gender and age are expected to display similar effects as in other social contexts. Hypothesis 4. Gender: Individuals of the same gender are more likely to interact with one another than those of opposite genders. Hypothesis 5. Age: Individuals who have smaller age differences are more likely to interact with one another than those who have bigger differences. We expect that players usually interact with others who joined the virtual world at similar time periods. Individuals with similar game age, i.e. in the same group in a game, usually have similar levels of knowledge, status, tenure, and the same goals in the virtual world. New players can design their characters, learn basic functions in the world, and meet other fellow players. In addition, players joining at the same time period are presented with the same “version” of the world and the same player population, which further enhances the perception of them being similar. Hypothesis 6. Game age: Players who enter a virtual world during the same time period are more likely to interact with one another than those who have bigger differences in starting time. To summarize, spatial proximity, temporal proximity, and homophily all establish similar effects on forming and enabling interactions between individuals. In general, when people are physically close to each other, located in similar time zones, and have similar social and demographic attributes, they are more likely to start interacting with each other and have more frequent communication. ''21.3. Methods '' '' '' In this study, the impact of spatial proximity, temporal proximity, and homophily are examined in a large virtual world—EverQuest II, a massively multiplayer online role-playing game (MMORPG) launched in November of 2004. EverQuest II operates virtual game worlds based on individual game servers. For most activities, players are only allowed to interact with other players who are on the same server. Transfer of characters from one server to another is not encouraged and necessitates a charge. As a result, a server can be considered as an independent virtual world with a stable population of players. This study examines player interactions on the Guk server. In the game, each player can create one or more characters (or avatars) and each character needs to develop combat skills to kill monsters. In order to advance levels faster, players can team up with others to fight monsters. After analysis of the data from EverQuest II, players' online relations in the game are identified based on their collaboration activities and precise measures of spatial proximity, temporal proximity, and homophily are constructed. The effects of proximity and homophily on virtual world networks are analysed through cross-sectional network analyses. ''21.3.1. Data samples—partnership in EverQuest II '' A detailed server log from May 1, 2006 to September 11, 2006 was provided by Sony for analysis. The data describes players' demographic information and collaborative activities that occurred in a sever called the Guk server. The Guk server is a typical player-versus-environment (PvE) server which focusses on killing monsters, or non-player characters (NPC)s. EverQuest II allows players to form groups among themselves in order to play together and efficiently. As in the case of offline friendship, two players can be considered as partners if they are in a group together and earn experience points in combat collaboration activities. The partnership relation is an important aspect because this form of collaboration represents a stronger dyadic relation between two players than the interactions in bigger groups. Here, partnership is defined as a binary and undirected tie between two players if they use their characters to achieve more than two outcomes together. A player could establish partnership relations with others through different game characters. Data samples are extracted from the log data to test the overall effect of proximity and homophily among all players in a given time period. Because the Guk server is designed to host players in North America, only players in the United States and Canada are included in the samples. From September 5, 2006 to September 11, 2006, 1525 unique players who partnered with others (1478 in the United States and 47 in Canada) are identified and their partnership network is illustrated in Fig. 1. ''21.3.2. Measurements '' The detailed activity records obtained from EverQuest II are used to build relation networks, represented by an adjacency matrix with 1525 nodes and 1179 edges (network density 0.5%). This partnership network is used as the dependent variable in ERG models. On entering in EverQuest IIfor the first time, players are required to report their demographic information such as gender, date of birth, and address zip code. The players' zip codes and country codes are used to estimate their offline location and to construct distance and time zone differences between players. The individual attributes such as gender, age, and game age (based on the dates of registration) are used to construct the homophily measures between players. ''21.3.2.1. Distance '' In order to calculate distance, the players' zip codes and country codes are first mapped to latitude/longitude using ZIPList5 and Canada Geocode databases from ZipInfo.com. The shortest distance between any two players is calculated using their latitude and longitude coordinates according to Spherical law of cosines (Eq. (1)): Dij = a cos(sin(lati) * sin(latj) + cos(lati) *cos(latj) * cos(longj-longi))*6371km ---(1) The marginal impact of distance on interactions between two locales declines significantly as the distance between them increases. For example, the impact of distance between 800 km away and 850 km away is very small and the difference is much bigger between 50 km and 100 km. As a result, there are four categorical measures and one continuous measure developed based on the raw distance to capture the non-linear impact of distance. The categorical measures include four binary matrices: Same_zip_code, Short_distance, Medium_distance, and Long_distance. If player i and j are located in the same zip code, Same_zip_codeij equals one. Based on the study on human travel by Brockmann et al. 2, Short_distanceij, Medium_distanceij, and Long_distanceij are used to indicate whether the distance between two players is smaller than 50 km (but not in the same zip code), between 50 and 800 km, or more than 800 km. Short distance is a range that can be reached for daily activities and long distance is a range with places out of a geographical region. The geographic distribution of players in the sample is consistent with the U.S. Census data and most of them are located far away from each other: only 0.05% pairs of them are located in the same zip code, 0.6% are in short distance, 15% are in medium distance, and the rest are in long distance. However, players in partner relations tend to be much closer to each other: in 20.9% of partner relations two players live in the same zip code and in 9.7% of relations players live in a short distance. Kleinberg 5 suggested that the tie probability should be a negative exponential function of distance. The continuous measure is constructed using an exponential decay function to measure the decreasing effect of distance (Eq. (2)). If two players are located in the same time zone, the impact of distance between them equals one, which indicates the maximal impact between the two; if the distance is d0, the distance impact is reduced to 0.368. In this study, we use 50 km as d0. Distanceimpactij = EXP( −dij/d0) ---(2) ''21.3.2.2. Timezone_difference '' Similarly the players' zip codes can be mapped into time zones. The time zone difference between two players is the absolute value hour difference between their time zones. Three individual attribute variables include Gender, Age, and Game_age. Gender is a binary variable indicating whether a player is female. Age is calculated at the time point September 11, 2006. Game_age is the number of months each individual played since registration. Table 1 shows the descriptive statistics of individual locations and attributes in the sample set. 19% of the players are female having an average age of 33.63. The similarity of the attributes is measured in three matrices Based on Gender, Age, and Game_age variables: Same_gender, indicates whether two players have the same gender, Age_difference, indicates the age difference between players, and Game_Age_differernce, indicates the game age difference between players. '' '' ''21.3.3. Analyses '' The assumption in many statistical models is that relational ties among a given set of nodes are independent even though some relations are affected by others. For example, certain popular users have many ties and friends of friends become friends themselves. Exponential Random Graph Models (p*/ERGM) explicitly incorporate the dependence of the relations within a network by considering the observed network as one realization of a network generation process and estimate how likely the observed structure emerges out of all possible configurations generated in the process. Therefore, we can draw inferences of multiple factors that could be associated with the likelihood of a partnership tie existing between two players: attributes of players (e.g., gender, age and game age), joint attributes of two players (e.g., gender homophily), and relational attributes between two players (e.g., distance). In the analysis, Same_zip_code, Short_distance, Medium_distance, Long_distance, and Distance_impact are used as measures of spatial proximity to test Hypotheses 1 and 2. Timezone_difference as a measure of temporal proximity to test Hypothesis 3. Same_gender, Age_difference, and Game_Age_differernce are as a measure of homophily to test Hypotheses 4, 5, and 6. Gender(Female), Age, and Game_Age are used as baseline control variables. The estimated coefficients with positive coefficients indicate that the corresponding attributes or structures are more likely to occur than by random chance, and negatives indicate less likely. The effect size of one additional unit is measured by the odds ratio (OR), which is equal to the exponential function of the corresponding coefficient, e.g. eβ. While examining the impacts of the exogenous factors on the formation of online relations, ERG models control for the endogenous factors that enable and constrain the formation. In ERG models, to control for sparsity, popularity, and transitivity, three network statistics were included: the number of edges (Edges) that indicate the network density; the geometrically weighted degree distribution (GWDegree) that summarizes the degree distribution in a network; and geometrically weighted edgewise shared partners (GWESP) that measures the number of players connecting two other players in a network 4,10. Four ERG models are estimated to understand the marginal contributions of the explanatory variables. Model 0, is a baseline model which includes six control variables; Model 1 estimates the impacts of temporal proximity as well as homophily; Model 2 combines Distance_impact and Timezone_difference to estimate the impact of spatial proximity and temporal proximity at the same time; Model 3 uses Same_zip_code and Short_distance (taking Medium_distance and Long_distance as the base category) to study the detailed impact of spatial proximity. Statnet 15 v2.2-3 with R-2.10.1 is used for estimation. ''21.4. Results '' Table 2 shows the results of the ERG models, which assess the impact of homophily and the relative importance of different ranges of offline distance and network structures in partnership networks. The edge parameter controls the density of a network. The significant and negative coefficients suggest that partnership relations in EverQuest II are sparse and individuals usually do not engage in interaction randomly. As an anti-preferential attachment measure, the positive impact of geometrically weighted degree distribution (GWDegree) tells us that popular players who have many relations are usually less likely to engage in a partnership with others. We note that the degrees of the players, i.e., numbers of partners to an individual are evenly distributed when compared to a random network with the same density and over effects modeled. The positive coefficients of geometrically weighted edgewise shared partners (GWESP) tell us that the partnership in the game is transitive, which suggests that if two players have common partners they will most likely become partners with each other. Model 1 shows the impact of time difference: the odds ratio of becoming partners for two players within a one-hour difference is 61% of the odds ratio of players in the same time zone. Hypothesis 3 on temporal proximity is supported. Model 2 examines the impact of time zone differences controlling for distance. Given the impact of distance,we see that the time zone differences reduce the likelihood of interaction This is seen from the negative and significant coefficient of time zone differences. This is also seen in Model 2 from the positive coefficient of distance impact. If two players are located closer offline, i.e., if the distance impact between them is larger, there is a greater chance for them to be partners online. From the proximity part of Model 3 we can the positive and significant impacts of Same_zip_code and Short_distance taking Medium_distance and Long_distance as the baselines. We can deduce from this that two players in the same zip code are more likely to form relations than two players within a short distance (less than 50 km but not in the same zip code). Similarly, short distance relations are more likely to be formed than medium distance relations, which are more likely than long distance relations. As an example, we can see in Model 3, the odds ratio of partnership formation between players living in the same zip code is 721 times more compared to the odds ratios of players living more than 50 km apart. Also, players living within 50 km but not in the same zip code are 21.5 times more likely to be partners than the ones farther apart. The results show that players who are proximate in geographical distance are more likely to engage in interaction than those who are not proximate. Moreover, close proximity has a substantially bigger impact than medium or low proximity. Hypotheses 1 and 2 are supported. In all models, the negative coefficients of Age_difference and Game_age_difference support Hypotheses 5 and 6. Individuals tend to play with people who have similar age and join the game at the similar time i.e., have the similar level of online experience. Among the two, the game age difference, i.e., the difference in registration dates, has a bigger impact than age. On the other hand, the impact of gender homophily (Hypothesis 4) is not significant. There is no evidence supporting that individuals with the same gender are more likely to become partners. The goodness-of-fit diagnostics for Model 3 is illustrated in Fig. 2. The left-hand graph plots the degree distribution predicted by the Model 1b (gray lines) and the observed degree distribution (the solid line). The overall shape of the observed degree distribution is captured by the model, although it overestimates the number of isolates and underestimates the number of high degree nodes. This is because no isolates are included in the sample. The right-hand graph plots the edgewise shared partner distribution and the GWESP statistic generated by the estimated model captures the correct amount of clustering in the observed partnership network. The impact of distance, time zones, players' gender, age, and game age was analysed on the process of relation building in virtual worlds given the endogenous network structures of online ties. For differentiating the effects on various human interactions online and offline among distributed individuals, a more nuanced approach was suggested to examine the impact of proximity by decomposing the construct itself. From the results, one can observe that spatial proximity, temporal proximity, as well as homophily in age and game age have a significant impact on players' behaviour in creating online relations. However, there is no evidence, of gender homophily in EverQuest II. The proximity and homophily theories are still valid in virtual worlds. The findings of this study illuminate the complex interplay between spatial proximity, temporal proximity, and homophily. The migration of offline relations into online worlds is an important factor that brings offline proximity and homophily into virtual worlds. References: 1 T. Allen, Managing the Flow of Technology, MIT Press, Cambridge, MA, 1977. 2 D. Brockmann, L. Hufnagel, T. Geisel, The scaling laws of human travel, Nature 439 (2006) 462–465. 3 M.J. Culnan, M.L. Markus, Information technologies, in: F.M. Jablin, L. Putnam, K.H. Roberts, L.W. 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